The present invention pertains to viscosity detectors and particularly to delta-pressure-based sensors. More particularly, the invention pertains to viscosity sensors for determining the oxygen demand (for complete combustion) of a gaseous or liquid fuel for combustion purposes.
Existing and recently proposed quasi-static viscometers are either fluid (i.e., gas or liquid) density and pressure-dependent and costly (such as vibrating wire or quartz crystal-based viscometers). Other viscometers suffer from additional fluid property dependencies (e.g., those involving thermally-driven capillary flow), are prone to drift due to deteriorating and leaky valves (as in viscometers dependent on capillary flow driven by periodic refill from a source of pressurized gas, valve closure and decay observation), or depend on their orientation (as with the falling ball viscometer).
The proposed sensor measures a known property of fluids, viscosity. When applied to a combustion control system, it enables feed-forward operation and sensing in the mild pre-combustion environment; it is low-cost because the property can be simply proportional to the measured signal (in one preferred measurement approach) and it relates also simply to Wobbe number, oxygen demand or heating value of the fuel, so that the sensing error makes a relatively small contribution to the total combustion control error.
This invention involves the use or application of a known property, viscosity, to combustion control. It is also about using a preferred approach to viscosity measurement to that application.
Viscosity, .eta., may be known best for its linear relation to laminar volumetric flow (dV/dt) and pressure drop, .DELTA.p, in a capillary (of radius, r.sub.c, and length, L.sub.c), as shown in equation (1). EQU dV/dt=.pi..DELTA.pr.sub.c.sup.4 /(8L.sub.c.eta.) (1)
One first notes the potential of viscosity as an individual property for combustion control when searching for low-cost means to compensate for variabilities in natural gas composition, and for a way to determine heating value without combustion, which includes analytical determination via correlations involving k(T.sub.1), k(T.sub.2) and .eta., i.e., in conjunction with other properties.
Here, the viscosity of the fuel, and, previously, the stack O.sub.2 concentration were for indicating predicted or actual changes in the fuel's oxygen demand, D.sub.O2. FIG. 1 shows graphically a comparison between .eta., curve 23, and other fuel gas thermophysical (Q.sub.i) properties, i.e., .rho., density, curve 26; k, thermal conductivity, curve 24; c.sub.p, specific heat curve 25; and C.sub.v, thermal anemometer correction factor, curve 27; and how well they correlate individually with oxygen demand of fuel, D.sub.O2. .eta. exhibits a most advantageous, monotonic decrease as D.sub.O2 increases, although c.sub.p appears promising as well. The c.sub.p value of noncombustible CO.sub.2 (8.83 cal/(mol.multidot.K); 8.60 for H.sub.2 O) lies between that of CH.sub.4 and C.sub.2 H.sub.6 (8.50 and 12.42), but all .eta.-values of noncombustible gases O.sub.2, N.sub.2, CO.sub.2 (except H.sub.2 O) lie above that of CH.sub.4.
By including two or more fuel properties into a correlation with heating value or D.sub.O2, the achievable accuracy increases significantly (note cited art below), but at the penalty of significant cost increases as well, because of the need for digital processing for determination of c.sub.p. The above is based on the assumption that control of emissions and efficiency are prime goals of any combustion control; this is most closely achieved by operating under constant stack-O.sub.2 or excess air, which in turn is met by maintaining a constant air flow and adjusting fuel flow in response to its composition variations, which change D.sub.O2 and m*. Half of its density variation is taken care of by the factor m*, as it affects all orifice- or venturi-controlled flow control situations. The aim of adjusting fuel flow to counter variabilities in Wb, Wobb number, is similar but less correct (if one aims at conserving the A/F (air-to-fuel ratio) and emissions) and goes back to the definition of the Wobbe number, Wb=.DELTA.H/m*, with .DELTA.H=heating value rather than O.sub.2 demand and m*=(M.sub.gas /M.sub.air).sup.0.5. M is moles, Wb is closely aligned with Bn (Bonne number=D.sub.O2 /m*), as long as non-hydrocarbon fuel constituents such as H.sub.2 and CO are absent. A correlation of D.sub.O2 or Bn with viscosity may be determined with a formula D.sub.O2 =A+B.eta..sup.C or Bn=A'+B'.eta..sup.0.5, respectively. A and B are correlation coefficients and C is a correlation exponent. A' and B' are similarly correlation coefficients. The correlation is like that of natural law. Related information is in FIG. 6, page 21, of "Microsensors for Fluid Properties", by U. Bonne and D. Kubisiak, Scientific Honeyweller, Sensors Issue (1996). Additional information is in U.S. Pat. No. 5,486,107 by U. Bonne, issued Jan. 23, 1996 and entitled "Determination of Fuel Characteristics", which is herein incorporated by reference.
To illustrate the significance of the proposed, viscometer-based combustion control system, Table 1 compares some parameters relevant to the quality of a combustion control system based on thermal conductivity versus viscosity sensors. As shown, on all counts, the viscosity-based system lists more advantageous values such as smaller sensor output dependence on pressure and temperature but larger dependence fuel-gas composition or fuel concentration in a fuel+air mixture. The latter parameter was included to quantify the merits of direct measurement of thermo-physical properties of the fuel+air mixtures; as shown, measurement of viscosity or thermal conductivity in a premixed fuel+air mixture makes the pressure, temperature and humidity effects much larger than the sought fuel property effects. A similar case can be made for the measurement of .eta. or k in the stack gases.
Table 1 indicates advantages of viscosity versus thermal conductivity as D.sub.O2 or .lambda., wavelength, sensors. .lambda.=(actual fuel/air ratio).div.(stoichiometric air/fuel ratio). This table indicates that viscosity is approximately two times more sensitive to changes in .lambda. and D.sub.O2 than thermal conductivity, but thirty percent less sensitive to variations in pressure and temperature. That means viscosity detection results in a several times more accurate sensor than thermal conductivity, for D.sub.O2 or .lambda. measurement. The gas G20 is methane and G271 is a gas mixture of 74 percent methane and 26 percent nitrogen. p is pressure in bars, and T, temperature, is in degrees Celsius. W is the dependent variable, measuring the desired property (.lambda. or D.sub.O2). Sensitivities of k and .eta. are relative to variability in nitrogen content of fuel mixed with air, .lambda., T, p and nitrogen content of pure fuel gas.
TABLE 1 .differential.W/.differential.x W = k W = .eta. Dependence Conditions % % 1. .differential.W(.lambda.)/.differential. (fuel + air) G20 + air vs G271 + air 0.2687 -0.3532 .lambda.= 1.05; 15.degree. C. 2. .differential.W(.lambda.)/.differential..lambda. .lambda.= 1.05 vs. 1.10 0.0930 -0.1229 G20 + air 3. .differential.W(D.sub.o2)/.differential.Gas G20 vs G271 (26% N.sub.2) 6.7490 -13.782 15.degree. C.; 1 bar 4. .differential.W(D.sub.o2)/.differential.T T = 20 vs T = 15.degree. C.; G20 1.6320 1.3860 5. .differential.W(D.sub.o2)/.differential.P P = 2 vs 1 bar; G20; 0.1938 0.1043
For the most desirable property (k or .eta.), the values of W for rows 1-3 should be the highest and 4-5 the lowest. Viscosity is obviously the preferred choice.